* Step 1: Sum WORST_CASE(Omega(n^1),O(n^1))
    + Considered Problem:
        - Strict TRS:
            active(adx(X)) -> adx(active(X))
            active(adx(cons(X,Y))) -> mark(incr(cons(X,adx(Y))))
            active(hd(X)) -> hd(active(X))
            active(hd(cons(X,Y))) -> mark(X)
            active(incr(X)) -> incr(active(X))
            active(incr(cons(X,Y))) -> mark(cons(s(X),incr(Y)))
            active(nats()) -> mark(adx(zeros()))
            active(tl(X)) -> tl(active(X))
            active(tl(cons(X,Y))) -> mark(Y)
            active(zeros()) -> mark(cons(0(),zeros()))
            adx(mark(X)) -> mark(adx(X))
            adx(ok(X)) -> ok(adx(X))
            cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
            hd(mark(X)) -> mark(hd(X))
            hd(ok(X)) -> ok(hd(X))
            incr(mark(X)) -> mark(incr(X))
            incr(ok(X)) -> ok(incr(X))
            proper(0()) -> ok(0())
            proper(adx(X)) -> adx(proper(X))
            proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
            proper(hd(X)) -> hd(proper(X))
            proper(incr(X)) -> incr(proper(X))
            proper(nats()) -> ok(nats())
            proper(s(X)) -> s(proper(X))
            proper(tl(X)) -> tl(proper(X))
            proper(zeros()) -> ok(zeros())
            s(ok(X)) -> ok(s(X))
            tl(mark(X)) -> mark(tl(X))
            tl(ok(X)) -> ok(tl(X))
            top(mark(X)) -> top(proper(X))
            top(ok(X)) -> top(active(X))
        - Signature:
            {active/1,adx/1,cons/2,hd/1,incr/1,proper/1,s/1,tl/1,top/1} / {0/0,mark/1,nats/0,ok/1,zeros/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {active,adx,cons,hd,incr,proper,s,tl
            ,top} and constructors {0,mark,nats,ok,zeros}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            active(adx(X)) -> adx(active(X))
            active(adx(cons(X,Y))) -> mark(incr(cons(X,adx(Y))))
            active(hd(X)) -> hd(active(X))
            active(hd(cons(X,Y))) -> mark(X)
            active(incr(X)) -> incr(active(X))
            active(incr(cons(X,Y))) -> mark(cons(s(X),incr(Y)))
            active(nats()) -> mark(adx(zeros()))
            active(tl(X)) -> tl(active(X))
            active(tl(cons(X,Y))) -> mark(Y)
            active(zeros()) -> mark(cons(0(),zeros()))
            adx(mark(X)) -> mark(adx(X))
            adx(ok(X)) -> ok(adx(X))
            cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
            hd(mark(X)) -> mark(hd(X))
            hd(ok(X)) -> ok(hd(X))
            incr(mark(X)) -> mark(incr(X))
            incr(ok(X)) -> ok(incr(X))
            proper(0()) -> ok(0())
            proper(adx(X)) -> adx(proper(X))
            proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
            proper(hd(X)) -> hd(proper(X))
            proper(incr(X)) -> incr(proper(X))
            proper(nats()) -> ok(nats())
            proper(s(X)) -> s(proper(X))
            proper(tl(X)) -> tl(proper(X))
            proper(zeros()) -> ok(zeros())
            s(ok(X)) -> ok(s(X))
            tl(mark(X)) -> mark(tl(X))
            tl(ok(X)) -> ok(tl(X))
            top(mark(X)) -> top(proper(X))
            top(ok(X)) -> top(active(X))
        - Signature:
            {active/1,adx/1,cons/2,hd/1,incr/1,proper/1,s/1,tl/1,top/1} / {0/0,mark/1,nats/0,ok/1,zeros/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {active,adx,cons,hd,incr,proper,s,tl
            ,top} and constructors {0,mark,nats,ok,zeros}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          adx(x){x -> mark(x)} =
            adx(mark(x)) ->^+ mark(adx(x))
              = C[adx(x) = adx(x){}]

** Step 1.b:1: Bounds WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            active(adx(X)) -> adx(active(X))
            active(adx(cons(X,Y))) -> mark(incr(cons(X,adx(Y))))
            active(hd(X)) -> hd(active(X))
            active(hd(cons(X,Y))) -> mark(X)
            active(incr(X)) -> incr(active(X))
            active(incr(cons(X,Y))) -> mark(cons(s(X),incr(Y)))
            active(nats()) -> mark(adx(zeros()))
            active(tl(X)) -> tl(active(X))
            active(tl(cons(X,Y))) -> mark(Y)
            active(zeros()) -> mark(cons(0(),zeros()))
            adx(mark(X)) -> mark(adx(X))
            adx(ok(X)) -> ok(adx(X))
            cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
            hd(mark(X)) -> mark(hd(X))
            hd(ok(X)) -> ok(hd(X))
            incr(mark(X)) -> mark(incr(X))
            incr(ok(X)) -> ok(incr(X))
            proper(0()) -> ok(0())
            proper(adx(X)) -> adx(proper(X))
            proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
            proper(hd(X)) -> hd(proper(X))
            proper(incr(X)) -> incr(proper(X))
            proper(nats()) -> ok(nats())
            proper(s(X)) -> s(proper(X))
            proper(tl(X)) -> tl(proper(X))
            proper(zeros()) -> ok(zeros())
            s(ok(X)) -> ok(s(X))
            tl(mark(X)) -> mark(tl(X))
            tl(ok(X)) -> ok(tl(X))
            top(mark(X)) -> top(proper(X))
            top(ok(X)) -> top(active(X))
        - Signature:
            {active/1,adx/1,cons/2,hd/1,incr/1,proper/1,s/1,tl/1,top/1} / {0/0,mark/1,nats/0,ok/1,zeros/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {active,adx,cons,hd,incr,proper,s,tl
            ,top} and constructors {0,mark,nats,ok,zeros}
    + Applied Processor:
        Bounds {initialAutomaton = perSymbol, enrichment = match}
    + Details:
        The problem is match-bounded by 10.
        The enriched problem is compatible with follwoing automaton.
          0_0() -> 1
          0_1() -> 17
          0_2() -> 28
          0_3() -> 39
          0_4() -> 45
          0_5() -> 56
          0_6() -> 79
          0_7() -> 103
          active_0(1) -> 2
          active_0(7) -> 2
          active_0(8) -> 2
          active_0(9) -> 2
          active_0(14) -> 2
          active_1(1) -> 24
          active_1(7) -> 24
          active_1(8) -> 24
          active_1(9) -> 24
          active_1(14) -> 24
          active_2(16) -> 25
          active_2(17) -> 25
          active_3(33) -> 32
          active_4(27) -> 37
          active_4(41) -> 42
          active_5(36) -> 43
          active_5(57) -> 50
          active_6(55) -> 51
          active_6(62) -> 63
          active_7(58) -> 64
          active_7(78) -> 69
          active_8(77) -> 72
          active_8(87) -> 88
          active_9(86) -> 89
          active_9(108) -> 97
          active_10(110) -> 111
          adx_0(1) -> 3
          adx_0(7) -> 3
          adx_0(8) -> 3
          adx_0(9) -> 3
          adx_0(14) -> 3
          adx_1(1) -> 18
          adx_1(7) -> 18
          adx_1(8) -> 18
          adx_1(9) -> 18
          adx_1(14) -> 18
          adx_1(16) -> 15
          adx_2(27) -> 26
          adx_2(29) -> 25
          adx_3(27) -> 33
          adx_3(34) -> 32
          adx_4(36) -> 41
          adx_4(37) -> 32
          adx_4(38) -> 40
          adx_5(43) -> 42
          adx_5(44) -> 47
          adx_6(46) -> 61
          adx_6(51) -> 50
          adx_6(54) -> 76
          adx_6(55) -> 57
          adx_7(54) -> 67
          adx_7(58) -> 62
          adx_7(64) -> 63
          adx_7(73) -> 71
          adx_7(81) -> 85
          adx_7(98) -> 95
          adx_8(80) -> 75
          adx_8(104) -> 101
          adx_8(105) -> 107
          cons_0(1,1) -> 4
          cons_0(1,7) -> 4
          cons_0(1,8) -> 4
          cons_0(1,9) -> 4
          cons_0(1,14) -> 4
          cons_0(7,1) -> 4
          cons_0(7,7) -> 4
          cons_0(7,8) -> 4
          cons_0(7,9) -> 4
          cons_0(7,14) -> 4
          cons_0(8,1) -> 4
          cons_0(8,7) -> 4
          cons_0(8,8) -> 4
          cons_0(8,9) -> 4
          cons_0(8,14) -> 4
          cons_0(9,1) -> 4
          cons_0(9,7) -> 4
          cons_0(9,8) -> 4
          cons_0(9,9) -> 4
          cons_0(9,14) -> 4
          cons_0(14,1) -> 4
          cons_0(14,7) -> 4
          cons_0(14,8) -> 4
          cons_0(14,9) -> 4
          cons_0(14,14) -> 4
          cons_1(1,1) -> 19
          cons_1(1,7) -> 19
          cons_1(1,8) -> 19
          cons_1(1,9) -> 19
          cons_1(1,14) -> 19
          cons_1(7,1) -> 19
          cons_1(7,7) -> 19
          cons_1(7,8) -> 19
          cons_1(7,9) -> 19
          cons_1(7,14) -> 19
          cons_1(8,1) -> 19
          cons_1(8,7) -> 19
          cons_1(8,8) -> 19
          cons_1(8,9) -> 19
          cons_1(8,14) -> 19
          cons_1(9,1) -> 19
          cons_1(9,7) -> 19
          cons_1(9,8) -> 19
          cons_1(9,9) -> 19
          cons_1(9,14) -> 19
          cons_1(14,1) -> 19
          cons_1(14,7) -> 19
          cons_1(14,8) -> 19
          cons_1(14,9) -> 19
          cons_1(14,14) -> 19
          cons_1(17,16) -> 15
          cons_2(28,27) -> 26
          cons_2(30,29) -> 25
          cons_3(28,27) -> 33
          cons_3(31,27) -> 33
          cons_3(35,34) -> 32
          cons_3(39,36) -> 38
          cons_4(39,36) -> 41
          cons_4(45,46) -> 44
          cons_4(48,49) -> 43
          cons_5(45,46) -> 55
          cons_5(52,53) -> 51
          cons_6(45,61) -> 60
          cons_6(56,54) -> 58
          cons_6(56,76) -> 77
          cons_7(56,67) -> 66
          cons_7(70,71) -> 68
          cons_7(79,85) -> 86
          cons_7(83,84) -> 82
          cons_8(74,75) -> 72
          cons_8(91,92) -> 90
          cons_8(93,94) -> 88
          cons_8(96,92) -> 108
          cons_9(99,100) -> 97
          cons_9(106,109) -> 110
          hd_0(1) -> 5
          hd_0(7) -> 5
          hd_0(8) -> 5
          hd_0(9) -> 5
          hd_0(14) -> 5
          hd_1(1) -> 20
          hd_1(7) -> 20
          hd_1(8) -> 20
          hd_1(9) -> 20
          hd_1(14) -> 20
          incr_0(1) -> 6
          incr_0(7) -> 6
          incr_0(8) -> 6
          incr_0(9) -> 6
          incr_0(14) -> 6
          incr_1(1) -> 21
          incr_1(7) -> 21
          incr_1(8) -> 21
          incr_1(9) -> 21
          incr_1(14) -> 21
          incr_6(60) -> 59
          incr_7(66) -> 65
          incr_7(68) -> 63
          incr_7(76) -> 84
          incr_7(77) -> 78
          incr_8(72) -> 69
          incr_8(85) -> 92
          incr_8(86) -> 87
          incr_8(95) -> 94
          incr_9(89) -> 88
          incr_9(101) -> 100
          incr_9(107) -> 109
          mark_0(1) -> 7
          mark_0(7) -> 7
          mark_0(8) -> 7
          mark_0(9) -> 7
          mark_0(14) -> 7
          mark_1(15) -> 2
          mark_1(15) -> 24
          mark_1(18) -> 3
          mark_1(18) -> 18
          mark_1(20) -> 5
          mark_1(20) -> 20
          mark_1(21) -> 6
          mark_1(21) -> 21
          mark_1(23) -> 12
          mark_1(23) -> 23
          mark_2(26) -> 25
          mark_3(38) -> 37
          mark_4(40) -> 32
          mark_4(44) -> 43
          mark_5(47) -> 42
          mark_6(59) -> 50
          mark_7(65) -> 63
          mark_7(82) -> 69
          mark_8(90) -> 88
          nats_0() -> 8
          nats_1() -> 17
          nats_2() -> 31
          ok_0(1) -> 9
          ok_0(7) -> 9
          ok_0(8) -> 9
          ok_0(9) -> 9
          ok_0(14) -> 9
          ok_1(16) -> 10
          ok_1(16) -> 24
          ok_1(17) -> 10
          ok_1(17) -> 24
          ok_1(18) -> 3
          ok_1(18) -> 18
          ok_1(19) -> 4
          ok_1(19) -> 19
          ok_1(20) -> 5
          ok_1(20) -> 20
          ok_1(21) -> 6
          ok_1(21) -> 21
          ok_1(22) -> 11
          ok_1(22) -> 22
          ok_1(23) -> 12
          ok_1(23) -> 23
          ok_2(27) -> 29
          ok_2(28) -> 30
          ok_2(31) -> 30
          ok_3(33) -> 25
          ok_3(36) -> 34
          ok_3(39) -> 35
          ok_4(41) -> 32
          ok_4(45) -> 48
          ok_4(46) -> 49
          ok_5(54) -> 53
          ok_5(54) -> 73
          ok_5(55) -> 43
          ok_5(56) -> 52
          ok_5(56) -> 70
          ok_6(57) -> 42
          ok_6(58) -> 51
          ok_6(76) -> 71
          ok_6(77) -> 68
          ok_6(79) -> 74
          ok_6(81) -> 80
          ok_6(81) -> 98
          ok_7(62) -> 50
          ok_7(78) -> 63
          ok_7(85) -> 75
          ok_7(85) -> 95
          ok_7(86) -> 72
          ok_7(96) -> 93
          ok_7(103) -> 102
          ok_7(105) -> 104
          ok_8(87) -> 69
          ok_8(92) -> 94
          ok_8(106) -> 99
          ok_8(107) -> 101
          ok_8(108) -> 88
          ok_9(109) -> 100
          ok_9(110) -> 97
          proper_0(1) -> 10
          proper_0(7) -> 10
          proper_0(8) -> 10
          proper_0(9) -> 10
          proper_0(14) -> 10
          proper_1(1) -> 24
          proper_1(7) -> 24
          proper_1(8) -> 24
          proper_1(9) -> 24
          proper_1(14) -> 24
          proper_2(15) -> 25
          proper_2(16) -> 29
          proper_2(17) -> 30
          proper_3(26) -> 32
          proper_3(27) -> 34
          proper_3(28) -> 35
          proper_4(36) -> 49
          proper_4(39) -> 48
          proper_4(40) -> 42
          proper_5(38) -> 43
          proper_5(45) -> 52
          proper_5(46) -> 53
          proper_5(47) -> 50
          proper_6(44) -> 51
          proper_6(59) -> 63
          proper_7(45) -> 70
          proper_7(46) -> 73
          proper_7(54) -> 98
          proper_7(60) -> 68
          proper_7(61) -> 71
          proper_7(65) -> 69
          proper_8(54) -> 80
          proper_8(56) -> 74
          proper_8(66) -> 72
          proper_8(67) -> 75
          proper_8(76) -> 95
          proper_8(81) -> 104
          proper_8(82) -> 88
          proper_8(83) -> 93
          proper_8(84) -> 94
          proper_9(79) -> 102
          proper_9(85) -> 101
          proper_9(90) -> 97
          proper_9(91) -> 99
          proper_9(92) -> 100
          s_0(1) -> 11
          s_0(7) -> 11
          s_0(8) -> 11
          s_0(9) -> 11
          s_0(14) -> 11
          s_1(1) -> 22
          s_1(7) -> 22
          s_1(8) -> 22
          s_1(9) -> 22
          s_1(14) -> 22
          s_7(56) -> 83
          s_7(79) -> 96
          s_8(74) -> 93
          s_8(79) -> 91
          s_8(103) -> 106
          s_9(102) -> 99
          tl_0(1) -> 12
          tl_0(7) -> 12
          tl_0(8) -> 12
          tl_0(9) -> 12
          tl_0(14) -> 12
          tl_1(1) -> 23
          tl_1(7) -> 23
          tl_1(8) -> 23
          tl_1(9) -> 23
          tl_1(14) -> 23
          top_0(1) -> 13
          top_0(7) -> 13
          top_0(8) -> 13
          top_0(9) -> 13
          top_0(14) -> 13
          top_1(24) -> 13
          top_2(25) -> 13
          top_3(32) -> 13
          top_4(42) -> 13
          top_5(50) -> 13
          top_6(63) -> 13
          top_7(69) -> 13
          top_8(88) -> 13
          top_9(97) -> 13
          top_10(111) -> 13
          zeros_0() -> 14
          zeros_1() -> 16
          zeros_2() -> 27
          zeros_3() -> 36
          zeros_4() -> 46
          zeros_5() -> 54
          zeros_6() -> 81
          zeros_7() -> 105
** Step 1.b:2: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            active(adx(X)) -> adx(active(X))
            active(adx(cons(X,Y))) -> mark(incr(cons(X,adx(Y))))
            active(hd(X)) -> hd(active(X))
            active(hd(cons(X,Y))) -> mark(X)
            active(incr(X)) -> incr(active(X))
            active(incr(cons(X,Y))) -> mark(cons(s(X),incr(Y)))
            active(nats()) -> mark(adx(zeros()))
            active(tl(X)) -> tl(active(X))
            active(tl(cons(X,Y))) -> mark(Y)
            active(zeros()) -> mark(cons(0(),zeros()))
            adx(mark(X)) -> mark(adx(X))
            adx(ok(X)) -> ok(adx(X))
            cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
            hd(mark(X)) -> mark(hd(X))
            hd(ok(X)) -> ok(hd(X))
            incr(mark(X)) -> mark(incr(X))
            incr(ok(X)) -> ok(incr(X))
            proper(0()) -> ok(0())
            proper(adx(X)) -> adx(proper(X))
            proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
            proper(hd(X)) -> hd(proper(X))
            proper(incr(X)) -> incr(proper(X))
            proper(nats()) -> ok(nats())
            proper(s(X)) -> s(proper(X))
            proper(tl(X)) -> tl(proper(X))
            proper(zeros()) -> ok(zeros())
            s(ok(X)) -> ok(s(X))
            tl(mark(X)) -> mark(tl(X))
            tl(ok(X)) -> ok(tl(X))
            top(mark(X)) -> top(proper(X))
            top(ok(X)) -> top(active(X))
        - Signature:
            {active/1,adx/1,cons/2,hd/1,incr/1,proper/1,s/1,tl/1,top/1} / {0/0,mark/1,nats/0,ok/1,zeros/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {active,adx,cons,hd,incr,proper,s,tl
            ,top} and constructors {0,mark,nats,ok,zeros}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(Omega(n^1),O(n^1))